Founding mathematics on semantic conventions / / Casper Storm Hansen
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| Autore: |
Hansen Casper Storm
|
| Titolo: |
Founding mathematics on semantic conventions / / Casper Storm Hansen
|
| Pubblicazione: | Cham, Switzerland : , : Springer, , [2021] |
| ©2021 | |
| Descrizione fisica: | 1 online resource (259 pages) |
| Disciplina: | 510.1 |
| Soggetto topico: | Mathematics - Philosophy |
| Logic, Symbolic and mathematical | |
| Semantics (Philosophy) | |
| Filosofia de la matemàtica | |
| Lògica matemàtica | |
| Soggetto genere / forma: | Llibres electrònics |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | Intro -- Founding Mathematics on Semantic Conventions -- Preface -- Contents -- 1 Introduction -- 1.1 Overview and Guide to Partial Reading -- 2 Classical Mathematics and Plenitudinous Combinatorialism -- 2.1 Large Cardinal Axioms and Theorems of Arithmetic -- 2.2 Transfinite Ordinals -- 2.3 Transfinite Cardinals -- 2.4 The Continuum Hypothesis -- 3 Intuitionism and Choice Sequences -- 3.1 General Introduction -- 3.2 Brouwer on Freely Proceeding Choice Sequences -- 3.3 Constitution of Free Choice Sequences -- 3.4 Evaluation of Brouwer's Claim -- 3.5 Verificationism and Intuitionistic Logic -- 4 From Logicism to Predicativism -- 4.1 Frege -- 4.2 Russell -- 4.3 Weyl -- 4.4 Weyl's Failure to Include All Real Numbers -- 5 Conventional Truth -- 5.1 The Obvious Solution to the Liar Paradox -- 5.2 Conventional Truth Conditions -- 5.3 The Dogma -- 5.4 Possible Language Conventions -- 5.5 T-schemas and Expressive Strength -- 5.6 Dialectical Situation -- 5.7 The View from Nowhere -- 5.8 Comparison with Chihara's Position -- 5.9 Revenge -- 6 Semantic Conventionalism for Mathematics -- 6.1 Needs Assessment -- 6.2 Simple Arithmetic as a Conventional Language -- 6.3 Quine's Anti-Conventionalism -- 6.4 Rule-Following -- 6.5 Choice of Logic -- 7 A Convention for a Type-free Language -- 7.1 The Kripke Convention and Its Shortcomings -- 7.2 Reformulating the Kripke Convention -- 7.2.1 Collapsing Truth and Satisfaction of View-From-Nowhere Truth Conditions -- 7.2.2 Kleenification -- 7.2.3 Kripke Recursion -- 7.3 Adding a Conditional with Supervaluational Semantics -- 7.3.1 Supervaluation over All Possibilities -- 7.3.2 View-From-Nowhere Truth Conditions for the Strong Conditional -- 7.3.3 If the Supervaluation Criterion is Not Satisfied -- 7.3.4 Ensuring Quantification over All Possibilities in the Presence of Supervaluation. |
| 7.3.5 Iteration of the Strong Conditional -- 7.3.6 Summary -- 7.4 Denoting Terms for Applied Mathematics -- 7.5 Meta-Theorems -- 8 Basic Mathematics -- 8.1 Logic -- 8.2 Natural Numbers -- 8.3 Integers -- 8.4 Rational Numbers -- 8.5 Classicality So Far -- 8.6 Classes -- 8.7 An Example of Applied Mathematics -- 9 Real Analysis -- 9.1 Functions -- 9.2 Real Numbers -- 9.3 Exponentiation -- 9.4 Completeness -- 9.5 Suprema, Infima, and Roots -- 9.6 Continuity -- 9.7 Operations on Functions -- 9.8 Differentiation -- 9.8.1 Calculating Derivatives -- 9.8.2 Uniform Differentiability -- 9.9 Integration -- 9.10 Unbounded Intervals and Piecewise Continuity -- 9.11 Completifications of Functions Generalized -- 9.12 Another Example of Applied Mathematics -- 9.13 Diagonalization -- 10 Possibility -- 10.1 All Possible Real Numbers -- 10.2 Modal Metaphysics -- 10.3 Conclusion -- References -- Index of Symbols -- General Index. | |
| Titolo autorizzato: | Founding Mathematics on Semantic Conventions |
| ISBN: | 3-030-88534-8 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910508469503321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Synthese Library